Les Bleus, who face Poland in the last 16 on Sunday, underperformed at the Education City stadium and only after Kylian Mbappe, Antoine Griezmann and Ousmane Dembele came off the bench did they pose any threat.
Chelsea, however, were unlucky after they were again denied by the woodwork.
Roundup of Champions League matches played on Wednesday night
Round-up of football matches played around Europe on Saturday.
Messi's damning assessment of the team came home to roost when the season re-started after the coronavirus stoppage and Barca surrendered the league title to Real Madrid, prompting the captain to launch a new tirade against the team.
Barcelona won their 27th LaLiga title and first for four years after a 4-2 win at city rivals Espanyol on Sunday.
Argentine, somehow, were ready for an emotional, nail-biting encounter, having already gone through a dress rehearsal in the same stadium against the Netherlands in the quarter-finals.
Aubameyang joined Arsenal from German club Borussia Dortmund in 2018 for a fee of around 58 million pounds ($79 million) as former manager Arsene Wenger's last signing.
"There are other steps and it starts on Wednesday. Let's be happy with what we've done tonight even if it's not enough. At least we broke the (defending champions') curse," he added.
Both players have been timed among the fastest in the game, with top speeds of around 36.5kpm (22.6 mph), but it is how quickly they get there that makes them different.
A summary of Wednesday's action in the Champions League quarter-finals first leg.
Barcelona suffered in the absence of the injured Lionel Messi as they drew 1-1 at home
France qualified for the quarter-finals of the Nations League despite a lacklustre goalless draw against Israel on Thursday.
World champions France are facing mounting injuries ahead of their Euro 2020 Round of 16 match against Switzerland on Monday, with coach Didier Deschamps struggling for options.
IMAGES from football matches played across leagues in Europe on Sunday.
Lionel Messi insisted his fifth-place finish in Monday's Ballon d'Or awards was not a motivating factor behind his sensational performance in Barcelona's 4-0 thrashing of local rivals Espanyol in La Liga on Saturday.
A majestic solo dribble shredded Chelsea's defence before Messi played in Dembele for the second and the Argentine maestro killed the tie off when he smashed a third through the legs of Courtois again in the second half.
A summary of Sunday's action in the FIFA World Cup qualifiers across Europe.
France hoping Mbappe will be enough to match England's impressive depth
Giroud, at 36, brings experience and guile to France's attack, while Mbappe, 23, is blessed with pace
Southampton's 15 million pound ($19.19 million) purchase of Lazio centre back Wesley Hoedt brought the overall spend by England's 20 elite clubs to a record 1.184.9 billion pounds.
'There is no price limit to let him go or a price that we are ready to give in'
The French, who won their second world title in July, take on hosts Germany in the inaugural Nations League competition, their first game since the World Cup final against Croatia.
Roundup of the matches being held across major football leagues in Europe on Sunday
Borussia Dortmund missed a bagful of chances to draw 1-1 at home with Augsburg on Tuesday, as they squandered the opportunity to make up ground in the Bundesliga title race heading into the winter break.
Barcelona travel to newly-promoted Osasuna without their first choice front line.
Bundesliga leaders Bayern Munich stumbled to a 1-1 home draw against Hoffenheim on Saturday but stayed three points clear at the top as Borussia Dortmund's Pierre-Emerick Aubameyang fired four goals past Hamburg SV following his midweek ban. Bayern fell a goal behind when Kerem Demirbay's thundering shot in the 16th minute left keeper Manuel Neuer rooted on the spot.
Pierre-Emerick Aubameyang missed a penalty before scoring an 80th-minute equaliser as an injury-hit Borussia Dortmund failed to win for the second straight game after stumbling to a 1-1 home draw against Hertha Berlin on Friday.
Kylian Mbappe believes Les Bleus have what it takes to win the title in Russia if they all stick together.
France's probable starting line-up for World Cup final
IMAGES from the UEFA Nations League matches played on Monday.
England forward Raheem Sterling joined Chelsea on a five-year contract from Manchester City, the two English Premier League clubs announced on Wednesday.
Costa turned Juanfran's low cross into the net in the 69th minute for Atletico's third goal in the first leg of the last 16 tie against third division Lleida but immediately limped to the sidelines. He did return to the pitch, however, and completed the game despite bleeding from his knee.
Messi opened the scoring at the Nou Camp with an audacious chipped penalty then restored control in the tie after Lyon had pulled a goal back to make it 2-1, hitting a decisive third goal after a trademark dazzling run to shake off four defenders.
Lionel Messi became Barca's record appearance maker in the competition with 76 Copa matches.
World champions France moved to four points while Hungary, on one point, kept up their slim hopes alive, in a group where they had been given little chance with heavyweights Germany and Portugal also in the mix.
Ansu Fati is the second-youngest player to represent the Catalan giants in La Liga aged 16 years and 298 days.
Manchester City squandered a three-goal lead to draw 3-3 with Feyenoord in the Champions League on Tuesday.
Alvaro Morata scored a brace to help Atletico Madrid deliver a statement performance as they outclassed city rivals Real Madrid.
Didier Deschamps has tough choices to make ahead of his young team's World Cup opener against Australia and the experienced Olivier Giroud could find himself on the bench.
